Let us remember that a metaphor is a form of comparison, an example of figurative language, that does not use the word "like" or "as." If we have a careful look at the story, one of the first metaphors that I can spot is used to describe the marriage of Rip Van Winkle and how having a "termagant wife" can impact a husband:

Their tempers, doubtless, are rendered pliant and malleable in the fiery furnace of domestic tribulation; and a curtain lecture is worth all the sermons in the world for teaching the virtues of patience and long-suffering.

Note how the marriage is compared to a "fiery furnace of domestic tribulation," clearly identifying the kind of troublesome nature of Rip's marriage and the way that he is being painfully refined because of his status as a "hen-pecked husband."

Symbols are objects, actions or characters that stand both for their literal meaning but also come to suggest some other symbolic meaning. A great example of a symbol in this excellent story is Rip himself, who is shown to be unaffected by the massive turbulent historical events that he has missed in his sleep. In fact, through the use of Rip symbolically, Irving manages to suggest that not that much has changed actually in essentials over the course of Rip's enchanted sleep. Note how Rip is described in the following quote:

Rip, in fact, was no politician; the changes of states and empires made but little impression on him; but there was one species of despotism under which he had long groaned, and that was—petticoat government.

Note the irony and humour of this comment. Irving effectively manages to write off the Revolution and the massive changes that accompanied it by stating that the oppression of men as experienced by them in their marriage is a far worse form of political existence than either before or after the Revolution.